JEE Main 2022 · 27 Jun · Shift 2 · Physics Q36

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PhysicsSingle correct+4 / -1Question 36 of 90

Four spheres each of mass $m$ form a square of side $d$ (as shown in figure). A fifth sphere of mass $M$ is situated at the centre of square. The total gravitational potential energy of the system is :

Four spheres of mass m at the corners of a square of side d, with a sphere of mass M at the centre.

-\dfrac{Gm}d\left[\left(4+\sqrt2\right)m+4\sqrt2M\right]

-\dfrac{Gm}d\left[\left(4+\sqrt2\right)M+4\sqrt2m\right]

-\dfrac{Gm}d\left[3m^2+4\sqrt2M\right]

-\dfrac{Gm}d\left[6m^2+4\sqrt2M\right]

Answer and worked solution

Official answer: A

Pairs. Four sides: $-\dfrac{4Gm^2}d$ . Two diagonals: $-\dfrac{2Gm^2}{\sqrt2d}=-\dfrac{\sqrt2Gm^2}d$ . Centre with each corner: $-\dfrac{4GMm}{d/\sqrt2}=-\dfrac{4\sqrt2GMm}d$ .

Total. $-\dfrac{Gm}d\left[(4+\sqrt2)m+4\sqrt2M\right]$ .

(A)

Topics:Gravitational field and potential

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JEE Main 2022 · 27 Jun · Shift 2, Physics question 36